Proofs of Two Conjectures On the Dimensions of Binary Codes

2010/01/28 by Junhua Wu, Wu, Junhua
Computer Science · Engineering · Mathematics · #05E18 #20C20 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #graph theory and CDMA systems #math.CO #math.RT #msc:05E18 #msc:20C20

paper · pdf · doi:10.48550/arxiv.1001.5077

29 pages

openalex publication_date 2010/01/28 · arxiv created 2011/04/02 · arxiv updated 2011/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L and L₀ be the binary codes generated by the column \mathbbF₂-null space of the incidence matrix of external points versus passant lines and internal points versus secant lines with respect to a conic in PG(2, q), respectively. We confirm the conjectures on the dimensions of L and L₀ using methods from both finite geometry and modular representation theory.

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